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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 182070.ee
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
182070.ee1 | 182070o2 | \([1, -1, 1, -1069458962, 13461793218321]\) | \(37769548376817211811066153/1011738331054080\) | \(3623618736521678684160\) | \([2]\) | \(70778880\) | \(3.6503\) | |
182070.ee2 | 182070o1 | \([1, -1, 1, -66758162, 210901606161]\) | \(-9186763300983704416553/47730830553907200\) | \(-170951644902771287654400\) | \([2]\) | \(35389440\) | \(3.3038\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 182070.ee have rank \(1\).
Complex multiplication
The elliptic curves in class 182070.ee do not have complex multiplication.Modular form 182070.2.a.ee
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.